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Brownian motion

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Brownian motion

Any of various physical phenomena in which some quantity is constantly undergoing small, random fluctuations. It was named for Robert Brown, who was investigating the fertilization process of flowers in 1827 when he noticed a “rapid oscillatory motion” of microscopic particles within pollen grains suspended in water. He later discovered that similar motions could be seen in smoke or dust particles suspended in air and other fluids. The idea that molecules of a fluid are constantly in motion is a key part of the kinetic theory of gases, developed by James Clerk Maxwell, Ludwig Boltzmann, and Rudolf Clausius (1822–88) to explain heat phenomena.



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He covers generalized Gronwall inequality and Bihari inequality, Brownian motions and stochastic intervals, analysis of Ito and Feynman-Kac formulas, the Ruzumikhin technique of the Lyapunov method, approximate solutions to stochastic differential equations according to Cauchy-Marayama and Carathedory methods.
This twin effect of hydrodynamic interaction and Brownian motion governs the circular swimming patterns of Caulobacter and many other microorganisms.
The section on developments in stochastic dynamics discusses fractional Brownian motion in finance, moment evolution of Gaussian and geometric Wiener diffusions, two-dimensional linear dynamic systems with small random terms, and a dynamic theory of stochastic movement of systems.
 
 
 
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